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Markov Chain Monte Carlo Methods - NMTP539

Title:	Metody Markov Chain Monte Carlo
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2017
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Michaela Prokešová, Ph.D.
Class:	Pravděp. a statistika, ekonometrie a fin. mat. M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP139
Interchangeability :	NSTP139
Is interchangeable with:	NSTP139

Annotation -

Last update: T_KPMS (19.04.2016)

Markov chains with general state space, geometric ergodicity. Gibbs sampler, Metropolis-Hastings algorithm, properties and applications.

Aim of the course -

Last update: T_KPMS (16.05.2013)

The course should give insight into the basics

of Markov chains with general state space which are necessary for

understanding the theoretical properties of MCMC methods. Students

should become familiar with commonly used MCMC algorithms and after

the course they should be able to apply those algorithms to problems

in Bayesian and spatial statistics.

Literature -

Last update: RNDr. Michaela Prokešová, Ph.D. (08.10.2015)

S. Brooks, A. Gelman, G. L. Jones, X. Meng (2011): Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC, Boca Raton.

D. Gamerman a H. F. Lopes (2006): Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd ed., Chapman & Hall/CRC, Boca Raton.

W. S. Kendall, F. Liang, L.-S. Wang (Eds.) (2005): Markov Chain Monte Carlo: Innovations and Applications, World Scientific, Singapore.

S. P. Meyn a R. L. Tweedie (2009): Markov Chains and Stochastic Stability, 2nd ed., Cambridge University Press, Cambridge.

C. P. Robert (2001): The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, druhé vydání, Springer, New York.

Teaching methods -

Last update: T_KPMS (16.05.2013)

Lecture+exercises.

Syllabus -

Last update: RNDr. Michaela Prokešová, Ph.D. (25.09.2020)

1. Examples of simulation methods.

2. Bayesian statistics, hierarchial models.

3. Examples of MCMC algorithms, Gibbs sampler, Metropolis-Hastings

algorithm.

4. Markov chains with general state space.

5. Ergodicity of MCMC algorithms.

6. Simulated annealing, perfect simulation.

7. Point processes, birth-death Metropolis-Hastings algorithm.

8. Further applications.